Answer:
Approximately 775,000.
Step-by-step explanation:
The number is almost in between 750,000 and 800,000. The number in the middle of these two is 775,000.
The answer is none of the lines intersect each other, because they are at the same slope, and they do not have a different slope for the lines to be intersected.
3/4 = 9/12
2/3 = 8/12
9/12 - 8/12 = 1/12
So Johnny ran for 1/12 of an hour longer than Angie.
The first solution is quadratic, so its derivative y' on the left side is linear. But the right side would be a polynomial of degree greater than 1, so this is not the correct choice.
The third solution has a similar issue. The derivative of √(x² + 1) will be another expression involving √(x² + 1) on the left side, yet on the right we have y² = x² + 1, so that the entire right side is a polynomial. But polynomials are free of rational powers, so this solution can't work.
This leaves us with the second choice. Recall that
1 + tan²(x) = sec²(x)
and the derivative of tangent,
(tan(x))' = sec²(x)
Also notice that the ODE contains 1 + y². Now, if y = tan(x³/3 + 2), then
y' = sec²(x³/3 + 2) • x²
and substituting y and y' into the ODE gives
sec²(x³/3 + 2) • x² = x² (1 + tan²(x³/3 + 2))
x² sec²(x³/3 + 2) = x² sec²(x³/3 + 2)
which is an identity.
So the solution is y = tan(x³/3 + 2).
The answer is 700 dollars, BRAINLIEST PLEASE
